Every few years, we seem to discover that some previously identified dinosaur species that were primarily terrestrial had a much greater capacity for aquatic locomotion than previously assumed. An example would be the Spinosaurus which, while able to, preferred not to walk on land due to their expected inability to balance on their hind legs for long periods of time. It's hard to tell how far they could swim (especially being amphibious), which is an important piece of information for this question since it would affect how they could spread to other neighbouring land masses; if majorly aquatic, with the ability to live (i.e. feed, rest) entirely in a body of water, they could have spread throughout all neighbouring parts of the ocean, dependent on the temperature ranges they could survive in.
Flying dinosaurs could have escaped easily from an island, though the effect of their escape would be limited by points of rest, food sources, and other landmasses nearby.
Totally terrestrial dinosaurs without the ability to traverse great distances of ocean would struggle to escape, so the only precautionary measures necessary would be prevention of smuggling them. However, in the case of smaller species of predatory dinosaur (e.g. Compsognathus, described by its associated wikipedia page as "the size of a turkey), much stricter measures would have to be in place to prevent them effectively becoming stowaways on tourist-transport vehicles, supply vehicles, and small watercraft operated by bad actors, which could enable potentially several specimens to reach other, larger landmasses and become invasive species.
It's definitely worth noting that because of the lack of information contained in fossils, eggs, faeces, and skin impressions, the writers and thus the fictional government bodies in all the Jurassic Park movies (incl. Jurassic World), the countermeasures could only have been as appropriate to the at-the-time understanding of the dinosaur species they were attempting to recreate.
If you factor out the writer-manufactured jeopardy that creates the drama in these films, a well prepared organisation for creating contingencies for these "resurrected" specimens could likely have covered all bases; air, land, and sea; smuggling, human error, coups by malicious foreign powers. They could have had emergency protocols in place both on the island and surrounding nations to neutralise any escaped specimens regardless of their mode of locomotion.
Of course, this is all quite speculative and you'd have to ask the writers themselves if they ever detailed the contingencies in their world-building process. It is also noted in the films' literature that the DNA used to recreate the extinct creatures is incomplete due to decay, and that they used modern reptilian DNA to fill in the gaps. How this would affect their ability to survive the modern world's atmosphere, utilise food sources (prey will have evolved a great deal since their natural reign), and otherwise survive is difficult to tell without the writers going into great detail about the biology of the specimens featured in the films.